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<p>Implements an FPRAS for approximating the volume of a set of high-dimensional objects. The algorithm is described in.  
 <a href="structshark_1_1_hypervolume_approximator.html#details">More...</a></p>

<p><code>#include &lt;<a class="el" href="_hypervolume_approximator_8h_source.html">shark/Algorithms/DirectSearch/Operators/Hypervolume/HypervolumeApproximator.h</a>&gt;</code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a6c7042a7e0d1550769cb7d841ff35c45" id="r_a6c7042a7e0d1550769cb7d841ff35c45"><td class="memTemplParams" colspan="2">template&lt;typename Archive &gt; </td></tr>
<tr class="memitem:a6c7042a7e0d1550769cb7d841ff35c45"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_approximator.html#a6c7042a7e0d1550769cb7d841ff35c45">serialize</a> (Archive &amp;archive, const unsigned int version)</td></tr>
<tr class="separator:a6c7042a7e0d1550769cb7d841ff35c45"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a87334159cdfae43c729c8dd02b738f1c" id="r_a87334159cdfae43c729c8dd02b738f1c"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_approximator.html#a87334159cdfae43c729c8dd02b738f1c">epsilon</a> () const</td></tr>
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<tr class="memitem:a370c3d68bbfbbec92d4ca0bcfb7e79dd" id="r_a370c3d68bbfbbec92d4ca0bcfb7e79dd"><td class="memItemLeft" align="right" valign="top">double &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_approximator.html#a370c3d68bbfbbec92d4ca0bcfb7e79dd">epsilon</a> ()</td></tr>
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<tr class="memitem:abfeab3928eff47a2869c542b0ed020dc" id="r_abfeab3928eff47a2869c542b0ed020dc"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_approximator.html#abfeab3928eff47a2869c542b0ed020dc">delta</a> () const</td></tr>
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<tr class="memitem:affebaaa12c8b2ebd803397c157a3ec81" id="r_affebaaa12c8b2ebd803397c157a3ec81"><td class="memItemLeft" align="right" valign="top">double &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_approximator.html#affebaaa12c8b2ebd803397c157a3ec81">delta</a> ()</td></tr>
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<tr class="memitem:ac1bad82402367342bcb101f5d20bdfbc" id="r_ac1bad82402367342bcb101f5d20bdfbc"><td class="memTemplParams" colspan="2">template&lt;typename Set , typename <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> &gt; </td></tr>
<tr class="memitem:ac1bad82402367342bcb101f5d20bdfbc"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_approximator.html#ac1bad82402367342bcb101f5d20bdfbc">operator()</a> (Set const &amp;points, <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> const &amp;refPoint)</td></tr>
<tr class="memdesc:ac1bad82402367342bcb101f5d20bdfbc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Executes the algorithm.  <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implements an FPRAS for approximating the volume of a set of high-dimensional objects. The algorithm is described in. </p>
<p>Bringmann, Karl, and Tobias Friedrich. "Approximating the volume of unions and intersections of high-dimensional geometric objects." Algorithms and Computation. Springer Berlin Heidelberg, 2008. 436-447.</p>
<p>The algorithm computes an approximation of the true Volume V, V' that fulfills </p><p class="formulaDsp">
\[ P((1-epsilon)V &lt; V&#39; &lt;(1+epsilon)V&#39;) &lt; 1-\delta \]
</p>
 
<p class="definition">Definition at line <a class="el" href="_hypervolume_approximator_8h_source.html#l00052">52</a> of file <a class="el" href="_hypervolume_approximator_8h_source.html">HypervolumeApproximator.h</a>.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#affebaaa12c8b2ebd803397c157a3ec81">&#9670;&#160;</a></span>delta() <span class="overload">[1/2]</span></h2>

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<p class="definition">Definition at line <a class="el" href="_hypervolume_approximator_8h_source.html#l00071">71</a> of file <a class="el" href="_hypervolume_approximator_8h_source.html">HypervolumeApproximator.h</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#abfeab3928eff47a2869c542b0ed020dc">&#9670;&#160;</a></span>delta() <span class="overload">[2/2]</span></h2>

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<p class="definition">Definition at line <a class="el" href="_hypervolume_approximator_8h_source.html#l00067">67</a> of file <a class="el" href="_hypervolume_approximator_8h_source.html">HypervolumeApproximator.h</a>.</p>

<p class="reference">Referenced by <a class="el" href="structshark_1_1_hypervolume_calculator.html#a58f7ff1cbe7c9ba7f7aa7562d11eabb9">shark::HypervolumeCalculator::approximationDelta()</a>, <a class="el" href="structshark_1_1_hypervolume_calculator.html#a089a678e12c3772b6e50abab495bdcc6">shark::HypervolumeCalculator::approximationDelta()</a>, and <a class="el" href="structshark_1_1_hypervolume_approximator.html#ac1bad82402367342bcb101f5d20bdfbc">operator()()</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#a370c3d68bbfbbec92d4ca0bcfb7e79dd">&#9670;&#160;</a></span>epsilon() <span class="overload">[1/2]</span></h2>

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<p class="definition">Definition at line <a class="el" href="_hypervolume_approximator_8h_source.html#l00063">63</a> of file <a class="el" href="_hypervolume_approximator_8h_source.html">HypervolumeApproximator.h</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#a87334159cdfae43c729c8dd02b738f1c">&#9670;&#160;</a></span>epsilon() <span class="overload">[2/2]</span></h2>

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<p class="definition">Definition at line <a class="el" href="_hypervolume_approximator_8h_source.html#l00060">60</a> of file <a class="el" href="_hypervolume_approximator_8h_source.html">HypervolumeApproximator.h</a>.</p>

<p class="reference">Referenced by <a class="el" href="structshark_1_1_hypervolume_calculator.html#a966d065ae8e3bd27a94c9f2edae7373b">shark::HypervolumeCalculator::approximationEpsilon()</a>, <a class="el" href="structshark_1_1_hypervolume_calculator.html#a3ad379a89066eb0490896b3d2a2415b8">shark::HypervolumeCalculator::approximationEpsilon()</a>, and <a class="el" href="structshark_1_1_hypervolume_approximator.html#ac1bad82402367342bcb101f5d20bdfbc">operator()()</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#ac1bad82402367342bcb101f5d20bdfbc">&#9670;&#160;</a></span>operator()()</h2>

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template&lt;typename Set , typename <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> &gt; </div>
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          <td>(</td>
          <td class="paramtype">Set const &amp;&#160;</td>
          <td class="paramname"><em>points</em>, </td>
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          <td class="paramtype"><a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> const &amp;&#160;</td>
          <td class="paramname"><em>refPoint</em>&#160;</td>
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<p>Executes the algorithm. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">points</td><td>The set \(S\) of points for which the following assumption needs to hold: \(\forall s \in S: \lnot \exists s&#39; \in S: f( s&#39; ) \preceq f( s ) \) </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">refPoint</td><td>The reference point \(\vec{r} \in \mathbb{R}^n\) for the hypervolume calculation, needs to fulfill: \( \forall s \in S: s \preceq \vec{r}\). . </td></tr>
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<p class="definition">Definition at line <a class="el" href="_hypervolume_approximator_8h_source.html#l00079">79</a> of file <a class="el" href="_hypervolume_approximator_8h_source.html">HypervolumeApproximator.h</a>.</p>

<p class="reference">References <a class="el" href="structshark_1_1_hypervolume_approximator.html#abfeab3928eff47a2869c542b0ed020dc">delta()</a>, <a class="el" href="namespaceshark_1_1random.html#aa64d4174eaf7111b03e0504eaa56b666">shark::random::discrete()</a>, <a class="el" href="namespaceshark.html#a7b70e475fc3fb175cdfe5f2130d8c2cd">shark::dominance()</a>, <a class="el" href="structshark_1_1_hypervolume_approximator.html#a87334159cdfae43c729c8dd02b738f1c">epsilon()</a>, <a class="el" href="namespaceshark.html#a9dd514911f0c8ea5d1e7d9c5da198c45affba12f914d31701ac2e13d6ed7212f4">shark::EQUIVALENT</a>, <a class="el" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">shark::random::globalRng</a>, <a class="el" href="namespaceshark.html#a9dd514911f0c8ea5d1e7d9c5da198c45a6b8a8f1e70649e457e42340e307475c3">shark::LHS_DOMINATES_RHS</a>, <a class="el" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>, <a class="el" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63">shark::sqr()</a>, and <a class="el" href="namespaceshark_1_1random.html#a18f302ea18f70835c59935973ba8ea84">shark::random::uni()</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#a6c7042a7e0d1550769cb7d841ff35c45">&#9670;&#160;</a></span>serialize()</h2>

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template&lt;typename Archive &gt; </div>
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          <td>(</td>
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<p class="definition">Definition at line <a class="el" href="_hypervolume_approximator_8h_source.html#l00055">55</a> of file <a class="el" href="_hypervolume_approximator_8h_source.html">HypervolumeApproximator.h</a>.</p>

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<hr/>The documentation for this struct was generated from the following file:<ul>
<li>include/shark/Algorithms/DirectSearch/Operators/Hypervolume/<a class="el" href="_hypervolume_approximator_8h_source.html">HypervolumeApproximator.h</a></li>
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